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Self-similar collapse of isothermal spheres and star formation
Abstract
Similarity solutions are obtained which describe the gravitational
collapse of isothermal spheres that originated as gas clouds not far
removed from the condition of marginal stability. It is argued that the
similarity solution of Larson and Penston (1969) for the stages before
core formation is physically artificial, but the gasdynamic flow
subsequent to core formation exhibits self-similar properties.
Similarity solutions are determined for the collapse of singular
isothermal spheres, minus solutions without critical points are obtained
by imposing the condition that the fluid velocities are negligible at
the 'initial instant', and an expansion-wave collapse solution is
evaluated. The results are illustrated with a numerical example roughly
corresponding to conditions appropriate for Bok globules or the central
regions of a nonmagnetic molecular cloud. Two possible applications of
the solutions are discussed: analyzing the stability to gravitational
fragmentation of collapsing pressure-free gas spheres and determining
the amount of energy radiated away during protostar formation.
... isothermal or polytropic) are well established in the literature (e.g. Larson (1969); Penston (1969); Hunter (1977); Shu (1977)). We mention in particular two similarity solutions: the first derived by Larson (1969) and Penston (1969) (hereafter referred to as the Larson-Penston solution) and the second by Shu (1977) (the Shu solution). ...
... Larson (1969); Penston (1969); Hunter (1977); Shu (1977)). We mention in particular two similarity solutions: the first derived by Larson (1969) and Penston (1969) (hereafter referred to as the Larson-Penston solution) and the second by Shu (1977) (the Shu solution). The former describes the highly dynamical collapse of a Bonnor-Ebert sphere, while the latter describes the quasi-static collapse of a singular isothermal sphere triggered by the propagation of a rarefaction wave after core formation. ...
... A widely adopted estimate (e.g. Hosokawa & Omukai (2009) In the Larson-Penston solution (which represents a highly dynamical isothermal collapse),Ṁ ≈ 47c 3 s /G (Hosokawa & Omukai 2009), while in the initially static Shu solution, the prefactor is very nearly unity (Shu 1977). Neither limit is typically attained in simulations (e.g. ...
We present an analytic description of the spherically symmetric gravitational collapse of radiatively cooling gas clouds. The approach is based on developing the "one-zone" density-temperature relationship of the gas into a full dynamical model. We convert this density-temperature relationship into a barotropic equation of state, which we use to calculate the density and velocity profiles of the gas. From these quantities we calculate the time-dependent mass accretion rate onto the center of the cloud. The approach clarifies the mechanism by which radiative cooling induces gravitational instability. In particular, we distinguish the rapid, quasi-equilibrium contraction of a cooling gas core to high central densities from the legitimate instability this contraction establishes in the envelope. We develop a refined criterion for the mass scale of this instability, based only on the chemical-thermal evolution in the core. We explicate our model in the context of a primordial mini-halo cooled by molecular hydrogen, and then provide two further examples, a delayed collapse with hydrogen deuteride cooling and the collapse of an atomic cooling halo. In all three cases, our results agree well with full hydrodynamical treatments.
... The low-mass star formation process has been extensively studied in the last 50 years. According to Shu (1977), gravitational collapse starts in a centrally concentrated configuration and spreads outward at the speed of sound (a); after a certain amount of time t, matter inside the infall radius (r inf = at) starts to fall inward in free-fall motion. The density distribution follows the r −2 law holds in the static or nearly static outer envelope and r −3/2 law holds for the freely falling inner envelope. ...
... This situation is known as inside-out collapse as the front of accretion expands radially outward in time. Since the inflow region expand outward, it was termed the inside-out collapse solution Shu (1977). Among some of the earlier studies, Shu (1977) studied star formation by gravitational collapse with an inside-out collapse process (Shu, 1977). ...
... Since the inflow region expand outward, it was termed the inside-out collapse solution Shu (1977). Among some of the earlier studies, Shu (1977) studied star formation by gravitational collapse with an inside-out collapse process (Shu, 1977). As gravitational collapse starts, matter falls toward the center and eventually reaches a free-fall speed. ...
Since molecules are ubiquitous in space, the study of the 'Molecular Universe' could unfold the mystery of the existing Interstellar medium. Star formation is linked to the chemical evolution processes. Thus, an analysis of the formation of stars coupled with the chemical evolution would give a clear insight into the entire process. For example, various evolutionary stages of star formation could be probed by observing various molecules. Chemical diagnostics of these regions could be used to extract the physical properties (e.g., density, temperature, ionization degree, etc.) of these regions. Radiative transfer calculations are worthwhile in estimating physical parameters of the region where molecules are detected. However, the radiative transfer calculations are limited due to insufficient molecular data, such as spectroscopic information or collisional excitation probabilities of many interstellar species. Complex organic molecules are detected in various environments ranging from the cold gas in prestellar cores to the warm gas on solar system scales close to individual protostars. A comparative study of the relative abundances of molecules could provide insights into the beginning of chemical complexity and the link to our solar system. In my thesis, I would mainly investigate the physical properties and kinematics of different star-forming regions using radiative transfer modeling. The observed spatial differentiation between various key molecules is used to explain their physical structure or evolution and various microphysical effects. In addition, some key molecules are used to study the various evolutionary phases. This simulated data is useful for interpreting the observed data of different telescopes like IRAM 30m, GBT, ALMA, Herschel, SOFIA, etc.
... This progression remains true in global-gravitational-collapse models, where core-density profiles evolve toward the SIS solution (Gómez et al. 2021). Post-formation of an accreting object, the SIS model predicts a transition radius that moves outward with time, shifting back to a more shallow, ρ ∝ r −3/2 density profile at small r as collapse proceeds from the inside-out (Shu 1977). The protostellar source MMS-1 in L1521F shows such a transition (Tokuda et al. 2016). ...
... where n 0 is the gas density at radius r 0 . This is the expected density profile for a SIS, and represents the envelopes of protostellar cores, where n(r) ∝ r −2 for all r (Larson 1969;Shu 1977). We choose a range of central densities such that the maximum density at 5 au is less than the density at which a FHSC would form (n ∼ 2 × 10 −11 cm −3 ; Larson 1969). ...
... A density profile n ∝ r −1 , transitioning to n ∝ r −2 , is similar to the predicted density profile of an SIS after collapse has begun, where n ∝ r −3/2 in the central region r < r 0 undergoing free-fall collapse (Shu 1977). The transition radius moves outward as the collapse proceeds ("inside-out" collapse). ...
We present new Atacama Large Millimeter/submillimeter Array (ALMA) continuum and NH 2 D, N 2 D ⁺ , and H 2 D ⁺ line emission at matched, ∼100 au resolution toward the dense star-forming cores SM1N and N6 within the Ophiuchus molecular cloud. We determine the density and temperature structure of SM1N based on radiative transfer modeling and simulated observations of the multiwavelength continuum emission at 0.8, 2, and 3 mm. We show that SM1N is best fit by either a broken power-law or Plummer-like density profile with high central densities ( n ∼ 10 ⁸ cm ⁻³ ), and an inner transition radius of only ∼80–300 au. The free-fall time of the inner region is only a few ×10 ³ yr. The continuum modeling rules out the presence of an embedded first hydrostatic core (FHSC) or protostar. SM1N is therefore a dynamically unstable but still starless core. We find that NH 2 D is likely depleted at high densities within SM1N. The nonthermal velocity dispersions increase from NH 2 D to N 2 H ⁺ and H 2 D ⁺ , possibly tracing increasing (but still subsonic) infall speeds at higher densities as predicted by some models of starless core contraction. Toward N6, we confirm the previous ALMA detection of a faint, embedded point source (N6-mm) in 0.8 mm continuum emission. NH 2 D and N 2 D ⁺ avoid N6-mm within ∼100 au, while H 2 D ⁺ is not strongly detected toward N6. The distribution of these tracers is consistent with heating by a young, warm object. N6-mm thus remains one of the best candidate FHSCs detected so far, although its observed (sub)millimeter luminosity remains below predictions for FHSCs.
... Another important observational and theoretical issue concerns the dynamical status of prestellar cores as they evolve to reach a high degree of central concentration. At one extreme, prestellar cores are viewed as quasi-static objects slowly evolving under magnetic support to reach the singular isothermal profile, which then undergoes near-pressureless collapse with a rarefaction wave propagating outward from the innermost region (Shu 1977). The other extreme is to treat the pressureless free-fall stage as beginning from a state with a flat density profile near the center, rather than a power law (Whitworth & Ward-Thompson 2001;Myers 2005). ...
... When the control volumes of two sink particles overlap each other, we merge them into a single particle created at the center of mass of the two merging particles, with the total mass and momentum being conserved. To verify that our sink particle implementation is correct, we repeat the test suites of the two-particle orbit, selfsimilar accretion of Shu (1977), and the Galilean invariance of accretion presented in Gong & Ostriker (2013a, Section 3.1, 3.2, 3.3). ...
A fundamental issue in star formation is understanding the precise mechanisms leading to the formation of prestellar cores, and their subsequent gravitationally unstable evolution. To address this question, we carefully construct a suite of turbulent, self-gravitating numerical simulations, and analyze the development and collapse of individual prestellar cores. We show that the numerical requirements for resolving the sonic scale and internal structure of anticipated cores are essentially the same in self-gravitating clouds, calling for the number of cells per dimension to increase quadratically with the cloud's Mach number. In our simulations, we follow evolution of individual cores by tracking the region around each gravitational potential minimum over time. Evolution in nascent cores is towards increasing density and decreasing turbulence, and there is a wide range of critical density for initiating collapse. At given spatial scale the turbulence level also varies widely, and tends to be correlated with density. By directly measuring the radial forces acting within cores, we identify a distinct transition to a state of gravitational runaway. We use our new theory for turbulent equilibrium spheres to predict the onset of each core's collapse. Instability is expected when the critical radius becomes smaller than the tidal radius; we find good agreement with the simulations. Interestingly, the imbalance between gravity and opposing forces is only during core collapse, meaning that this is a quasi-equilibrium rather than a free-fall process. For most of their evolution, cores exhibit both subsonic contraction and transonic turbulence inherited from core-building flows; supersonic radial velocities accelerated by gravity only appear near the end of the collapse.
... To model the toroidal field B ϕ , we note that there is a physical correlation between B r and B ϕ within the region of rapid collapse (i.e., inside the expansion wave front-see [19]). The region of strongly pinched magnetic field is also a region of strong twist in the magnetic field due to inward collapse with at least partial angular momentum conservation. ...
... Transformation to a cylindrical coordinate system is accomplished through r s = √ r 2 + z 2 , θ = tan −1 (r/z). We adopt β = −3/2, the typical power law index for gravitational collapse inside an outgoing expansion wave [19]. The factor sin n θ accounts for the cloud flattening and outflow cavity, similar to in models of magnetized toroids [13], and the index n can be adapted to fit the outflow zone calculated in simulations. ...
An hourglass-shaped magnetic field pattern arises naturally from the gravitational collapse of a star-forming gas cloud. Most studies have focused on the prestellar collapse phase, when the structure has a smooth and monotonic radial profile. However, most observations target dense clouds that already contain a central protostar, and possibly a circumstellar disk. We utilize an analytic treatment of the magnetic field along with insights gained from simulations to develop a more realistic magnetic field model for the protostellar phase. Key elements of the model are a strong radial magnetic field in the region of rapid collapse, an off-center peak in the magnetic field strength (a consequence of magnetic field dissipation in the circumstellar disk), and a strong toroidal field that is generated in the region of rapid collapse and outflow generation. A model with a highly pinched and twisted magnetic field pattern in the inner collapse zone facilitates the interpretation of magnetic field patterns observed in protostellar clouds.
... To model the toroidal field B ϕ , we note that there is a physical correlation between B r and B ϕ within the region of rapid collapse (i.e., inside the expansion wave front-see [19]). The region of strongly pinched magnetic field is also a region of strong twist in the magnetic field due to inward collapse with at least partial angular momentum conservation. ...
... Transformation to a cylindrical coordinate system is accomplished through r s = √ r 2 + z 2 , θ = tan −1 (r/z). We adopt β = −3/2, the typical power law index for gravitational collapse inside an outgoing expansion wave [19]. The factor sin n θ accounts for the cloud flattening and outflow cavity, similar to in models of magnetized toroids [13], and the index n can be adapted to fit the outflow zone calculated in simulations. ...
An hourglass-shaped magnetic field pattern arises naturally from the gravitational collapse of a star-forming gas cloud. Most studies have focused on the prestellar collapse phase, when the structure has a smooth and monotonic radial profile. However, most observations target dense clouds that already contain a central protostar, and possibly a circumstellar disk. We utilize an analytic treatment of the magnetic field along with insights gained from simulations to develop a more realistic magnetic field model for the protostellar phase. Key elements of the model are a strong radial magnetic field in the region of rapid collapse, an off-center peak in the magnetic field strength (a consequence of magnetic field dissipation in the circumstellar disk), and a strong toroidal field that is generated in the region of rapid collapse and outflow generation. A model with a highly pinched and twisted magnetic field pattern in the inner collapse zone facilitates the interpretation of magnetic field patterns observed in protostellar clouds.
... Because the angular momentum is conserved in the gravitational collapse process of the parent molecular cloud core, Equation (1) is also the protoplanetary disk + protostar system's total angular momentum. The gravitational collapse of a molecular cloud core has a self-similar solution [23], which gives the mass infall rate onto the protostellar disk + protostar system as ...
... We used the disk model proposed by Liu et al. [10]. In our disk model, we included the following physical mechanisms: the gravitational collapse of the parent molecular cloud core [23], the irradiation from the central star to the disk [19], the effect of the photoevaporation mechanism [13,14], the viscosity due to magnetorotational instability (MRI) [3] and gravitational instability (GI) [15][16][17], and the thermal ionization mechanism in the inner regions [18]. ...
In this paper, we investigate the mass accretion properties in the innermost regions of a viscously evolved protoplanetary disk and try to find some clues to the outburst events. In our newly developed one-dimensional time-dependent disk model based on the diffusion equation for surface density, we take into account the following physical effects: the gravitational collapse of the parent molecular cloud core, the irradiation from the central star to the disk, the effect of the photoevaporation mechanism, the viscosity due to the magnetorotational instability (MRI) and the gravitational instability (GI), and the thermal ionization mechanism in the inner regions. We find that the mass accretion rate M·disk in the innermost regions is statistically high enough to generate outbursts, although there are regions where the accretion rate is low. Additionally, we find that there is a weak correlation between the high mass accretion rate M·disk and the molecular cloud core’s properties (angular velocity ω and mass Mcd), as well as a strong correlation with the minimum viscosity parameter αmin. In general, there are two regions of outburst, the inner Region I and outer Region II. The outburst of Region I is caused by the MRI mechanism and thermal instability, while neither the MRI, the GI, nor the thermal instability causes the outburst of Region II. Our analysis suggests that the outer Region II is dominated by, or largely related to, the Rosseland mean opacity κR and the αmin parameter.
... The ambient envelope structure is characterized by the flattening and the poloidal field strength threading the singular isothermal toroid, labeled by n (see discussion in last sub-section 4.1, Shu 1996, andShang et al. 2006). The toroids evolve by increasing their deviation from the spherical singular isothermal sphere (Shu 1977), forming pseudodisks by flattening from the inner portions (as shown by Galli & Shu 1993;Allen et al. 2003;Väisälä et al. 2023). Allen et al. (2003) demonstrated how toroids open up as they evolve, determining the length-to-width ratios and opening angles of the resulting outflows. ...
The Atacama Large Millimeter/submillimeter Array Survey of Orion Planck Galactic Cold Clumps (ALMASOP) reveals complex nested morphological and kinematic features of molecular outflows through the CO (J = 2 - 1) and SiO (J = 5 - 4) emission. We characterize the jet and outflow kinematics of the ALMASOP sample in four representative sources (HOPS 10, 315, 358, and G203.21-11.20W2) through channel maps and position-velocity diagrams (PVDs) parallel and transverse to the outflow axes. The combined CO and SiO emission exhibits the coexistence of the conventional extremely-high-velocity (EHV) jets and shell-like low-velocity (LV) cavity walls and new features. More complex, nested bubble-like and filamentary structures in the images and channel maps, triangle-shaped regions near the base of the parallel PVDs, and regions composed of rhombus/oval shapes in the transverse PVDs, are also evident. Such features find natural explanations within the bubble structure of the unified model of jet, wind, and ambient medium. The reverse shock cavity is revealed on the PVD base regions, and other features naturally arise within the dynamic postshock region of magnetic interaction. The finer nested shells observed within the compressed wind region reveal previously unnoticed shocked emission between the jet and the conventional large cavity walls. These pseudopulse-produced filamentary features connect to the jet-like knotty blobs, creating an impression of episodicity in mass ejection. SiO emission is enhanced downstream of the reverse shock boundary, with jet-like excitation conditions. Combined, these observed features reveal the extended structures induced by the magnetic interplay between a jet-bearing magnetized wide-angle wind and its ambient magnetized surrounding medium.
... To evaluate the effects of resolution on our findings, we conducted a series of idealized tests of singular F. H. Shu (1977) collapse scenarios at resolutions of 10 −2 , 10 −3 , and 10 −4 M e . These tests track the problem hydrodynamically, allowing sink particle formation with subsequent accretion and radiation. ...
Stars form within dense cores composed of both gas and dust within molecular clouds. However, despite the crucial role that dust plays in the star formation process, its dynamics is frequently overlooked, with the common assumption being a constant, spatially uniform dust-to-gas ratio and grain size spectrum. In this study, we introduce a set of radiation-dust-magnetohydrodynamic simulations of star-forming molecular clouds from the STARFORGE project. These simulations expand upon the earlier radiation MHD models, which included cooling, individual star formation, and feedback. Notably, they explicitly address the dynamics of dust grains, considering radiation, drag, and Lorentz forces acting on a diverse size spectrum of live dust grains. We find that once stars exceed a certain mass threshold (∼2 M ⊙ ), their emitted radiation can evacuate dust grains from their vicinity, giving rise to a dust-suppressed zone of size ∼100 au. This removal of dust, which interacts with gas through cooling, chemistry, drag, and radiative transfer, alters the gas properties in the region. Commencing during the early accretion stages and preceding the main-sequence phase, this process results in a mass-dependent depletion in the accreted dust-to-gas (ADG) mass ratio within both the circumstellar disk and the star. We predict that massive stars (≳10 M ⊙ ) would exhibit ADG ratios that are approximately 1 order of magnitude lower than that of their parent clouds. Consequently, stars, their disks, and circumstellar environments would display notable deviations in the abundances of elements commonly associated with dust grains, such as carbon and oxygen.
... We also comment that Shu [47] criticized the Larson-Penston solution on physical grounds and proposed instead a certain "expanding wave" self-similar solution. Further, non-smooth, self-similar solutions were introduced by Summers and Whitworth [49] and were later argued to be unstable by Ori and Piran [42]. ...
Our result is a construction of infinitely many radial self-similar implosion profiles for the gravitational Euler–Poisson system. The problem can be expressed as solving a system of non-autonomous non-linear ODEs. The first rigorous existence result for a non-trivial solution to these ODEs is due to Guo et al. (Commun Math Phys 386(3):1551–1601, 2021), in which they construct a solution found numerically by Larson (Mon Not R Astron Soc 145(3):271–295, 1969) and Penston (Mon Not R Astron Soc 144(4):425–448, 1969) independently. The solutions we construct belong to a different regime and correspond to a strict subset of the family of profiles discovered numerically by Hunter (Astrophys J 218:834, 1977). Our proof adapts a technique developed by Collot et al. (Mem Am Math Soc 260(1255):v+97, 2019), in which they study blowup for a family of energy-supercritical focusing semilinear heat equations. In our case, the quasilinearity presents complications, most severely near the sonic point where the system degenerates.
... The findings demonstrate that the Jean mass fluctuates dramatically with density for a particular temperature range (20 K to 100 K), underscoring the vulnerability of gravitational stability to density fluctuations. The theoretical framework (Shu, 1977) states that . ...
The creation of stars and planetary systems depends on the gravitational collapse of solar nebulae. Comprehending the variables that impact this collapse, such as changes in temperature and density within molecular clouds, is essential to understanding the initial phases of star formation. This work aims to apply numerical simulations and theoretical models to examine the relationship between Jean's mass temperature and density variations in a solar nebula. The Jeans mass was determined in this study by running several simulations at various densities (10−20 kg/m³ to 10−15 kg/m³) and temperatures (10 K to 100 K). The conditions required for gravitational instability were visualized by modelling the gravitational potential, density, velocity, and magnetic field. Based on the data, it can be observed that the Jeans mass increases dramatically from 10 K to 100 K, reaching magnitudes of about 1.272×1033 kg at a density of 10−20 kg/m³. In addition, changes in density between 10−20 and 10−18 kg/m³ result in significant fluctuations in Jean's mass, especially between 20 and 100 K in temperature. The results demonstrate how vital temperature and density are in a molecular cloud's ability to remain stable in space. While the threshold mass for instability is lowered at higher densities, collapse at higher temperatures requires more enormous masses. These findings provide important new information about the mechanisms behind star formation and are consistent with theoretical forecasts and observational facts. Future research on more intricate physical processes, like radiative transmission and magnetic field dynamics, is advised to improve our comprehension of how stars emerge in molecular clouds.
... where c s is the sound speed and G is the gravitational constant (F. H. Shu 1977) because the density in dense cores is typically centrally concentrated and is not uniform (F. Motte & P. André 2001). ...
Protostellar disks around young protostars exhibit diverse properties, with their radii ranging from less than ten to several hundred astronomical units. To investigate the mechanisms shaping this disk radius distribution, we compiled a sample of 27 Class 0 and I single protostars with resolved disks and dynamically determined protostellar masses from the literature. Additionally, we derived the radial profile of the rotational-to-gravitational-energy ratio in dense cores from the observed specific angular momentum profiles in the literature. Using these observed protostellar masses and rotational energy profile, we computed theoretical disk radii from the hydrodynamic and nonideal magnetohydrodynamic (MHD) models in Y.-N. Lee et al. and generated synthetic samples to compare with the observations. In our theoretical model, the disk radii are determined by hydrodynamics when the central protostar+disk mass is low. After the protostars and disks grow and exceed certain masses, the disk radii become regulated by magnetic braking and nonideal MHD effects. The synthetic disk radius distribution from this model matches well with the observations. This result suggests that hydrodynamics and nonideal MHD can be dominant in different mass regimes (or evolutionary stages), depending on the rotational energy and protostar+disk mass. This model naturally explains the rarity of large (>100 au) disks and the presence of very small (<10 au) disks. It also predicts that the majority of protostellar disks have radii of a few tens of astronomical units, as observed.
... Observations find that protostellar envelopes have radii of several 1000 AU. Inferred from dust emission, the density profiles of the protostellar envelopes are often found following a radial density profile close to ρ ∝ r −2 (Looney et al., 2003;Maury et al., 2019), which is consistent with theoretical predictions described in , but steeper profile closer to ρ ∝ r −3/2 of the insideout collapse (Shu, 1977) is also observed (Kristensen et al., 2012). Dust properties are typically similar to the interstellar medium; however, in the inner envelope, signatures of grain growth can be observed (Galametz et al., 2019). ...
In this chapter, we will cover how stars form from the stellar nurseries that are giant molecular clouds. We will first review the physical processes that compete to regulate star formation. We then review star formation in turbulent, magnetized molecular clouds and the associated statistics giving rise to the star formation rate and the initial mass function of stars. We then present the protostellar stages in detail from an observational perspective. We will primarily discuss low-mass (<1.5\msun) stars. Finally, we examine how multiplicity complicates the single-star formation picture. This chapter will focus on star formation at redshift~0
... Most stars form in multiple systems (Offner et al. 2023), defying simple theoretical collapse models (Shu 1977). It is now recognized that in addition to gravity and thermal pressure, turbulence, magnetic fields, and interactions between the members of multiple systems all play a role in their formation (Murillo et al. 2016;Tychoniec et al. 2024). ...
We report the discovery of jets emanating from pre-main-sequence objects exclusively at mid-infrared wavelengths, enabled by the superb sensitivity of JWST's Mid-InfraRed Medium-Resolution Spectrometer (MIRI MRS) instrument. These jets are observed only in lines of [NiII], [FeII], [ArII], and [NeII]. The H emission, imaged in eight distinct transitions, has a completely different morphology, exhibiting a wide-angled, biconical shape, symmetrically distributed about the jet axes. Synergistic high-resolution Atacama Large Millimeter/submillimeter Array (ALMA) observations resolve a pair of side-by-side edge-on accretion disks lying at the origin of the twin mid-infrared jets. Assuming coevality of the components of the young multiple system under investigation, the system age is at least (2 2.5) 10 yr, despite the discrepantly younger age inferred from the spectral energy distribution of the combined edge-on disk sources. The later system evolutionary stage is corroborated by ALMA observations of CO(21), CO(2), and CO(21), which show no traces of molecular outflows or remnant cavity walls. Consequently, the observed H structures must have their origins in wide-angled disk winds, in the absence of any ambient, swept-up gas. In the context of recent studies of protostars, we propose an outflow evolutionary scenario in which the molecular gas component dominates in the youngest sources, whereas the fast, ionized jets dominate in the oldest sources, as is the case for the twin jets discovered in the WL 20 system.
... For p = 2, a constant velocity emerges, indicating a scalefree gravitational collapse (Li 2018), akin to the collapse of the envelope of a hydrostatic singular isothermal sphere (Shu 1977). However, when p < 2, u r increases as r decreases, suggesting that the collapse velocity accelerates down to smaller scales where star formation occurs. ...
The star formation efficiency (SFE) measures the proportion of molecular gas converted into stars, while the star formation rate (SFR) indicates the rate at which gas is transformed into stars. Here we propose such a model in the framework of a global radial collapse of molecular clouds, where the collapse velocity depends on the density profile and the initial mass-to-radius ratio of molecular clouds, with the collapse velocity accelerating during the collapse process. This simplified analytical model allows us to estimate a lifetime of giant molecular clouds of approximately , and a star formation timescale of approximately . Additionally, we can predict an SFE of approximately , and an SFR of roughly for the Milky Way in agreement with observations.
... where c s is the sound speed and G is the gravitational constant (Shu 1977), because the density in dense cores is typically centrally concentrated and is not uniform (Motte & André 2001). Though it is still a simplified assumption. ...
Protostellar disks around young protostars exhibit diverse properties, with their radii ranging from less than ten to several hundred au. To investigate the mechanisms shaping this disk radius distribution, we compiled a sample of 27 Class 0 and I single protostars with resolved disks and dynamically determined protostellar masses from the literature. Additionally, we derived the radial profile of the rotational to gravitational energy ratio in dense cores from the observed specific angular momentum profiles in the literature. Using these observed protostellar masses and rotational energy profile, we computed theoretical disk radii from the hydrodynamic and non-ideal magnetohydrodynamic (MHD) models in Lee et al. (2021, 2024) and generated synthetic samples to compare with the observations. In our theoretical model, the disk radii are determined by hydrodynamics when the central protostar+disk mass is low. After the protostars and disks grow and exceed certain masses, the disk radii become regulated by magnetic braking and non-ideal MHD effects. The synthetic disk radius distribution from this model matches well with the observations. This result suggests that hydrodynamics and non-ideal MHD can be dominant in different mass regimes (or evolutionary stages) depending on the rotational energy and protostar+disk mass. This model naturally explains the rarity of large (>100 au) disks and the presence of very small (<10 au) disks. It also predicts that the majority of protostellar disks have radii of a few tens of au, as observed.
... Assuming that the necessary conditions are present to avoid the fragmentation of gas into stars (generally temperatures 10 4 K and low metallicity; Oh & Haiman 2002), large amounts of pristine gas can be funneled into the central regions of a dark matter halo through, for example, the barswithin-bars instability (Shlosman et al. 1989(Shlosman et al. , 1990 or largescale magnetic torques (Begelman & Silk 2023;Hopkins et al. 2023). Depending on how efficiently angular momentum can be transported outward, a sufficiently large concentration of gas can be established on a short enough timescale to form a supermassive star that collapses due to a post-Newtonian instability (e.g., Hoyle & Fowler 1963;Fuller et al. 1986;Begelman 2010), but the details of this process are almost certainly more complicated than the spherically symmetric "Penston-Larson"-like models (e.g., Larson 1969;Penston 1969;Shu 1977;Whitworth & Summers 1985;Ogino et al. 1999) would suggest. An alternative is that the presence and distribution of angular momentum produces a more spatially distributed and centrifugally supported flow (i.e., a disk), resulting in a much smaller embryonic nuclear-burning region that contains a correspondingly smaller fraction of the mass of the collapsing cloud. ...
JWST observations demonstrate that supermassive black holes (SMBHs) exist by redshifts z ≳ 10, providing further evidence for “direct collapse” black hole (BH) formation, whereby massive (∼10 3–5 M ⊙ ) SMBH seeds are generated within a few million years as a byproduct of the rapid inflow of gas into the centers of protogalaxies. Here we analyze the intermediate “quasi-star” phase that accompanies some direct-collapse models, during which a natal BH accretes mass from and energetically sustains (through accretion) an overlying gaseous envelope. We argue that previous estimates of the maximum BH mass that can be reached during this stage, ∼1% of the total quasi-star mass, are unphysical, and arise from underestimating the efficiency with which energy can be transported outward from regions close to the BH. We construct new quasi-star models that consist of an inner, “saturated convection” region (which conforms to a convection-dominated accretion flow near the BH) matched to an outer, adiabatic envelope. These solutions exist up to a BH mass of ∼60% of the total quasi-star mass, at which point the adiabatic envelope contains only 2% of the mass (with the remaining ∼38% in the saturated-convection region), and this upper limit is reached within a time of 20–40 Myr. We conclude that quasi-stars remain a viable route for producing SMBHs at large redshifts, which is consistent with recent JWST observations.
... 4.2.2, a time-dependent collapse 711 profile can transition between different regimes, including from 712 subsonic to supersonic flows, or from WKB to freeze-out wave 713 regimes. It is thus necessary to study the effect of various col-714 lapse profiles, such as the typical profile of Shu (1977). instabilities of protostellar collapse, but also holds potential for 788 future adaptations to include MHD processes and dust dynamics 789 with more realistic collapse profiles. ...
We implement a local model for a spherical collapsing or expanding gas cloud in the Athena++ magnetohydrodynamic code. This local model consists of a Cartesian periodic box with time-dependent geometry. We present a series of benchmark test problems, including nonlinear solutions and linear perturbations of the local model, confirming the code's desired performance. During a spherical collapse, a horizontal shear flow is amplified, corresponding to angular momentum conservation of zonal flows in the global problem; wave speed and the amplitude of sound waves increase in the local frame, due to the reduction in the characteristic length scale of the box, which can lead to an anisotropic effective sound speed in the local box. Our code conserves both mass and momentum-to-machine precision. This numerical implementation of the local model has potential applications to the study of local physics and hydrodynamic instabilities during protostellar collapse, providing a powerful framework for better understanding the earliest stages of star and planet formation.
... As a result, these disks could grow in size more rapidly. Furthermore, in these sources, the dynamically collapsing region can extend to a 0.1 pc scale (Shu 1977;Sai et al. 2022). It is possible that the observed magnetic fields in these dense cores even on a 0.1 pc scale have been dragged around by the gas motions, which could result in the large misalignment angles, and may not represent the initial misalignment. ...
The magnetic field of a molecular cloud core may play a role in the formation of circumstellar disks in the core. We present magnetic field morphologies in protostellar cores of 16 targets in the Atacama Large Millimeter/submillimeter Array large program “Early Planet Formation in Embedded Disks (eDisk),” which resolved their disks with 7 au resolutions. The 0.1 pc scale magnetic field morphologies were inferred from the James Clerk Maxwell Telescope POL-2 observations. The mean orientations and angular dispersions of the magnetic fields in the dense cores are measured and compared with the radii of the 1.3 mm continuum disks and the dynamically determined protostellar masses from the eDisk program. We observe a significant correlation between the disk radii and the stellar masses. We do not find any statistically significant dependence of the disk radii on the projected misalignment angles between the rotational axes of the disks and the magnetic fields in the dense cores, nor on the angular dispersions of the magnetic fields within these cores. However, when considering the projection effect, we cannot rule out a positive correlation between disk radii and misalignment angles in three-dimensional space. Our results suggest that the morphologies of magnetic fields in dense cores do not play a dominant role in the disk formation process. Instead, the sizes of protostellar disks may be more strongly affected by the amount of mass that has been accreted onto star+disk systems, and possibly other parameters, for example, magnetic field strength, core rotation, and magnetic diffusivity.
... As shown in §4.2.2, a time-dependent collapse profile can transition between different regimes, including from subsonic to supersonic flows, or from WKB to freeze-out wave regimes. It is thus necessary to study the effect of various collapse profiles, such as the typical profile of Shu (1977). ...
We implement a local model for a spherical collapsing/expanding gas cloud into the Athena++ magnetohydrodynamic code. This local model consists of a Cartesian periodic box with time-dependent geometry. We present a series of benchmark test problems, including non-linear solutions and linear perturbations of the local model, confirming the code's desired performance. During a spherical collapse, a horizontal shear flow is amplified, corresponding to angular momentum conservation of zonal flows in the global problem; wave speed and amplitude of sound waves increase in the local frame, due to the reduction in the characteristic length scale of the box, which can lead to an anisotropic effective sound speed in the local box. Our code conserves both mass and momentum to machine precision. This numerical implementation of the local model has potential applications to the study of local physics and hydrodynamic instabilities during protostellar collapse, providing a powerful framework for better understanding the earliest stages of star and planet formation.
... The process of accretion is fundamental in the formation of stars even though it is poorly understood (Hartmann et al., 2016). Initially, a steady state accretion rate was theorized for the formation of stars (Larson, 1969;Shu, 1977;Terebey et al., 1984). However, the observed discrepancy in the luminosity of Class I young stellar objects (YSOs) with that of the theoretical models gave rise to the 'Luminosity Problem' (Kenyon et al., 1990;Evans et al., 2009). ...
We present here initial results of our spectro-photometric monitoring of XZ Tau. During our monitoring period, XZ Tau exhibited several episodes of brightness variations in timescales of months at optical wavelengths in contrast to the mid-infrared wavelengths. The color evolution of XZ Tau during this period suggests that the brightness variations are driven by changes in accretion from the disc. The mid-infrared light curve shows an overall decline in brightness by ∼ 0.5 and 0.7 magnitude respectively in WISE W1 (3.4 μm) and W2 (4.6 μm) bands. The emission profile of the hydrogen recombination lines along with that of Ca II IRT lines points towards magnetospheric accretion of XZ Tau. We have detected P Cygni profile in Hβ indicating of out-flowing winds from regions close to accretion. Forbidden transitions of oxygen are also detected, likely indicating jets originating around the central pre-main sequence star.
... To evaluate the effects of resolution on our findings, we conducted a series of idealized tests of singular Shu (1977) collapse scenarios at resolutions of 10 −2 , 10 −3 , and 10 −4 M ⊙ . These tests track the problem hydrodynamically, allowing sink particle formation with subsequent accretion and radiation. ...
Stars form within dense cores composed of both gas and dust within molecular clouds. However, despite the crucial role that dust plays in the star formation process, its dynamics is frequently overlooked, with the common assumption being a constant, spatially uniform dust-to-gas ratio and grain size spectrum. In this study, we introduce a set of radiation-dust-magnetohydrodynamic simulations of star forming molecular clouds from the {\small STARFORGE} project. These simulations expand upon the earlier radiation MHD models, which included cooling, individual star formation, and feedback. Notably, they explicitly address the dynamics of dust grains, considering radiation, drag, and Lorentz forces acting on a diverse size spectrum of live dust grains. We find that interactions between radiation and dust significantly influence the properties of gas surrounding and accreting onto massive stars. Specifically, we find that once stars exceed a certain mass threshold (), their emitted radiation can evacuate dust grains from their vicinity, giving rise to a dust-suppressed zone of size AU. Commencing during the early accretion stages and preceding the Main-sequence phase, this process results in a mass-dependent depletion in the accreted dust-to-gas (ADG) mass ratio within both the circumstellar disc and the star. We predict massive stars () would exhibit ADG ratios that are approximately one order of magnitude lower than that of their parent clouds. Consequently, stars, their discs, and circumstellar environments would display notable deviations in the abundances of elements commonly associated with dust grains, such as carbon and oxygen.
... These processes can lead to changes in the luminosity and color of the YSOs, with different patterns observed in the color-magnitude diagrams. Previous theoretical models proposed that protostars grow through a steady accretion of material (Shu 1977;Masunaga & Inutsuka 2000). However, recent research found that episodic accretion can contribute approximately half of the material accreted by protostars, making it an important component of the star formation process (Fischer et al. 2019). ...
This study focuses on the analysis of mid-infrared variability in a sample of high-mass young stellar objects (YSOs) associated with the cataloged sources from the APEX Telescope Large Area Survey of the Galaxy (ATLASGAL). The Near-Earth Object Wide-field Infrared Survey Explorer Reactivation Mission (NEOWISE) database was used to explore the long-term mid-infrared variability of these high-mass YSOs at a half-year scale. After matching with NEOWISE photometric measurements, a total of 2230 ATLASGAL sources were selected for the variability analysis, out of which 717 were identified as variables. The derived proportions of variables at different evolutionary stages show that the variability rate of high-mass YSOs is highest during the YSO stage and decreases with evolution toward the H ii region stage, resembling the behavior of low-mass YSOs. The variables can be classified into six types based on their light curves, divided into two categories: secular (linear, sin, sin+linear) and stochastic variables (burst, drop, and irregular). The magnitude–color variations observed in ∼160 secular variables can be mainly divided into “bluer when brighter/redder when dimming” and “redder when brighter/bluer when dimming,” likely originating from changes in accretion rate or the effect of extinction due to obscuration. Moreover, several episodic accretion candidates were selected for further observational studies.
... The ambipolar diffusion timescale is computed via Eq. (22) where each gas density is associated to a radius r assuming a Singular Isothermal Sphere (see Shu 1977) ρ = c 2 s 2πGr 2 . ...
The coupling between the magnetic field and the gas during the collapsing phase of star-forming cores is strongly affected by the dust size distribution, which is expected to evolve. We aim to investigate the influence of key parameters on the evolution of the dust distribution as well as on the magnetic resistivities during the protostellar collapse. We perform collapsing single zone simulations with shark. The code computes the evolution of the dust distribution, accounting for different grain growth and destruction processes. It also computes the magnetic resistivities. We find that the dust distribution significantly evolves during the protostellar collapse, shaping the magnetic resistivities. The peak size of the distribution, the population of small grains and consequently the magnetic resistivities are controlled by both coagulation and fragmentation rates. Under standard assumptions, the small grains coagulate very early as they collide by ambipolar drift, yielding magnetic resistivities orders of magnitude away from the non-evolving dust case. In particular, the ambipolar resistivity \eta_AD is very high prior to nH=10^10 cm^-3, and as a consequence magnetic braking should be ineffective. In this case, large size protoplanetary disks should result, which is inconsistent with recent observations. To alleviate this tension, we identify mechanisms to reduce the ambipolar resistivity during the protostellar collapse. The most promising are namely: electrostatic repulsion and grain-grain erosion. The evolution of the magnetic resistivities during the protostellar collapse and consequently the shape of the magnetic field in the early life of the protoplanetary disk strongly depends on the possibility to repopulate the small grains or to prevent their early coagulation. Therefore, it is crucial to better constrain the collision outcomes and the dust grain elastic properties.
... Protostars tend to be less luminous on average than they should be according to the 'final' stellar mass distribution. This was first noted in 1977 by[128] and is called the luminosity problem. ...
Young stellar objects (YSOs) accrete up to half of their material in short periods of enhanced mass accretion. For massive YSOs (MYSOs with more than 8 solar masses), accretion outbursts are of special importance, as they serve as diagnostics in highly obscured regions. Within this work, two outbursting MYSOs within different evolutionary stages, the young source G358.93-0.03 MM1 (G358) and the more evolved one G323.46-0.08 (G323), are investigated, and the major burst parameters are derived. For both sources, follow-up observations with the airborne SOFIA observatory were performed to detect the FIR afterglows. All together, we took three burst-/post-observations in the far infrared. The burst parameters are needed to understand the accretion physics and to conclude on the possible triggering mechanisms behind it. Up to today, G323s burst is the most energetic one ever observed for a MYSO. G358s burst was about two orders of magnitude weaker and shorter (2 months instead of 8 years). We suggest that G358s burst was caused by the accretion of a spiral fragment (or a small planet), where G323 accreted a heavy object (a planet or even a potential companion). To model those sources, we use radiative transfer (RT) simulations (static and time-dependent). G323s accretion burst is the first astrophysical science case, that is modeled with time-dependent RT (TDRT). We incorporate a small TDRT parameter-study and develop a time-depending fitting tool (the TFitter) for future modeling.
... As a result, these disks could grow in size more rapidly. Furthermore, in these sources, the dynamically collapsing region can extend to a 0.1 pc scale (Shu 1977;Sai et al. 2022). It is possible that the observed magnetic fields in these dense cores even on a 0.1 pc scale have been dragged around by the gas motions, which could result in the large misalignment angles, and may not represent the initial misalignment. ...
The magnetic field of a molecular cloud core may play a role in the formation of circumstellar disks in the core. We present magnetic field morphologies in protostellar cores of 16 targets in the Atacama Large Millimeter/submillimeter Array large program "Early Planet Formation in Embedded Disks (eDisk)", which resolved their disks with 7 au resolutions. The 0.1-pc scale magnetic field morphologies were inferred from the James Clerk Maxwell Telescope (JCMT) POL-2 observations. The mean orientations and angular dispersions of the magnetic fields in the dense cores are measured and compared with the radii of the 1.3 mm continuum disks and the dynamically determined protostellar masses from the eDisk program. We observe a significant correlation between the disk radii and the stellar masses. We do not find any statistically significant dependence of the disk radii on the projected misalignment angles between the rotational axes of the disks and the magnetic fields in the dense cores, nor on the angular dispersions of the magnetic fields within these cores. However, when considering the projection effect, we cannot rule out a positive correlation between disk radii and misalignment angles in three-dimensional space. Our results suggest that the morphologies of magnetic fields in dense cores do not play a dominant role in the disk formation process. Instead, the sizes of protostellar disks may be more strongly affected by the amount of mass that has been accreted onto star+disk systems, and possibly other parameters, for example, magnetic field strength, core rotation, and magnetic diffusivity.
... Accretion streamers have now been detected around many Class 0 and Class I sources and are relevant for improving our understanding of low-mass star formation. For instance, their discovery directly challenges the traditional model of axisymmetric collapse of protostellar cores (Shu 1977). The role accretion streamers play in episodic accretion processes still needs to be demonstrated; to our knowledge, no accretion streamers have been discovered around eruptive stars yet. ...
We present Atacama Large Millimeter/submillimeter Array 12-m, 7-m, and Total Power Array observations of the FU Orionis outbursting system, covering spatial scales ranging from 160 to 25,000 au. The high-resolution interferometric data reveal an elongated ¹² CO(2–1) feature previously observed at lower resolution in ¹² CO(3–2). Kinematic modeling indicates that this feature can be interpreted as an accretion streamer feeding the binary system. The mass infall rate provided by the streamer is significantly lower than the typical stellar accretion rates (even in quiescent states), suggesting that this streamer alone is not massive enough to sustain the enhanced accretion rates characteristic of the outbursting class prototype. The observed streamer may not be directly linked to the current outburst, but rather a remnant of a previous, more massive streamer that may have contributed enough to the disk mass to render it unstable and trigger the FU Orionis outburst. The new data detect, for the first time, a vast, slow-moving carbon monoxide molecular outflow emerging from this object. To accurately assess the outflow properties (mass, momentum, and kinetic energy), we employ ¹³ CO(2–1) data to correct for optical depth effects. The analysis indicates that the outflow corresponds to swept-up material not associated with the current outburst, similar to the slow molecular outflows observed around other FUor and Class I protostellar objects.
We modeled emissivities of the HCN and CO transitions across a grid of molecular cloud models encapsulating observed properties that span from normal star-forming galaxies to more extreme merging systems. These models are compared with archival observations of the HCN and CO transitions, in addition to the radio continuum at 93 GHz, for ten nearby galaxies. We combined these model emissivities with the predictions of gravoturbulent models of star formation presented in the first paper in this series. In particular, we explored the impact of excitation and optical depth on CO and HCN emission and assess if the HCN/CO ratio tracks the fraction of gravitationally bound dense gas, , in molecular clouds. We find that our modeled HCN/CO ratios are consistent with the measurements within our sample, and our modeled HCN and CO emissivities are consistent with the results of observational studies of nearby galaxies and clouds in the Milky Way. CO emission shows a wide range of optical depths across different environments, ranging from optically thick in normal galaxies to moderately optically thin in more extreme systems. HCN appears only moderately optically thick and shows significant subthermal excitation in both normal and extreme galaxies. We find an anticorrelation between HCN/CO and , which implies that the HCN/CO ratio is not a reliable tracer of . Instead, this ratio appears to best track gas at moderate densities (), which is below the typically assumed dense gas threshold of . We also find that variations in CO emissivity depend strongly on optical depth, which is a product of variations in the dynamics of the cloud gas. HCN emissivity is more strongly dependent on excitation, as opposed to optical depth, and thus does not necessarily track variations in CO emissivity. We further conclude that a single line ratio, such as HCN/CO, will not consistently track the fraction of gravitationally bound, star-forming gas if the critical density for star formation varies in molecular clouds. This work highlights important uncertainties that need to be considered when observationally applying an HCN conversion factor in order to estimate the dense (i.e.,\ cm $) gas content in nearby galaxies.
Context . The formation of stars has been subject to extensive studies in the past decades on scales from molecular clouds to proto-planetary disks. It is still not fully understood how the surrounding material in a protostellar system, which often shows asymmetric structures with complex kinematic properties, feeds the central protostar(s) and their disk(s).
Aims . We study the spatial morphology and kinematic properties of the molecular gas surrounding the IRS3A and IRS3B protostellar systems in the L1448N region located in the Perseus molecular cloud.
Methods . We present 1 mm Northern Extended Millimeter Array (NOEMA) observations of the large program PROtostars & DIsks: Global Evolution (PRODIGE). We analyzed the kinematic properties of molecular lines. Because the spectral profiles are complex, the lines were fit with up to three Gaussian velocity components. The clustering algorithm called density-based spatial clustering of applications with noise ( DBSCAN ) was used to disentangle the velocity components in the underlying physical structure.
Results . We discover an extended gas bridge (≈3000 au) surrounding both the IRS3A and IRS3B systems in six molecular line tracers (C ¹⁸ O, SO, DCN, H 2 CO, HC 3 N, and CH 3 OH). This gas bridge is oriented in the northeast-southwest direction and shows clear velocity gradients on the order of 100 km s ⁻¹ pc ⁻¹ toward the IRS3A system. We find that the observed velocity profile is consistent with analytical streamline models of gravitational infall toward IRS3A. The high-velocity C ¹⁸ O (2-1) emission toward IRS3A indicates a protostellar mass of ≈1.2 M ⊙ .
Conclusions . While high angular resolution continuum data often show IRS3A and IRS3B in isolation, molecular gas observations reveal that these systems are still embedded within a large-scale mass reservoir, whose spatial morphology and velocity profiles are complex. The kinematic properties of the extended gas bridge are consistent with gravitational infall toward the protostar IRS3A.
Identifying infall motions is crucial for our understanding of accretion processes in regions of star formation. The NH_ (1,1) hyperfine intensity anomaly (HIA) has been proposed to be a readily usable tracer for such infall motions in star-forming regions harboring young stellar objects at very early evolutionary stages. In this paper, we seek to study the HIA toward 15 infall candidate regions in order to assess its reliability as an infall tracer. Using deep observations of the NH_ (1,1) transition with the Effelsberg 100\,m telescope, we identified HIAs toward all 15 targets. Of the 15 sources, 14 exhibit anomalous intensities in either the inner or outer satellite lines. All the derived HIAs conform to the framework of the existing two models, namely hyperfine selective trapping (HST) and systematic contraction or expansion motion (CE) models. In our sample of infall candidates, the majority of the HIAs remain consistent with the HST model. Only in three targets are the HIAs consistent with infall motions under the CE model. Thus, the HIA could indeed be used as an infall tracer, but does not appear to be highly sensitive to infall motions in our single-dish data. Nevertheless, the emission could be blended with emission from outflow activities. HIAs consistent with the HST model show stronger anomalies with increasing kinetic temperatures K T_ K $. Therefore, HIAs may preferably trace the infall of cold gas.
Context. The formation and evolution of protoplanetary disks remains elusive. We have numerous astronomical observations of young stellar objects of different ages with their envelopes and/or disks. Moreover, in the last decade, there has been tremendous progress in numerical simulations of star and disk formation. New simulations use realistic equations of state for the gas and treat the interaction of matter and the magnetic field with the full set of nonideal magnetohydrodynamic (MHD) equations. However, it is still not fully clear how a disk forms and whether it happens from inside-out or outside-in. Open questions remain regarding where material is accreted onto the disk and comes from, how dust evolves in disks, and the timescales of appearance of disk’s structures. These unknowns limit our understanding of how planetesimals and planets form and evolve.
Aims. We attempted to reconstruct the evolutionary history of the protosolar disk, guided by the large amount of cosmochemical constraints derived from the study of meteorites, while using astronomical observations and numerical simulations as a guide to pinpointing plausible scenarios.
Methods. Our approach is highly interdisciplinary and we do not present new observations or simulations in this work. Instead, we combine, in an original manner, a large number of published results concerning young stellar objects observations, and numerical simulations, along with the chemical, isotopic and petrological nature of meteorites.
Results. We have achieved a plausible and coherent view of the evolution of the protosolar disk that is consistent with cosmochemical constraints and compatible with observations of other protoplanetary disks and sophisticated numerical simulations. The evidence that high-temperature condensates, namely, calcium-aluminum inclusions (CAIs) and amoeboid olivine aggregates (AOAs), formed near the protosun before being transported to the outer disk can be explained in two ways: there could have either been an early phase of vigorous radial spreading of the disk that occurred or fast transport of these condensates from the vicinity of the protosun toward large disk radii via the protostellar outflow. The assumption that the material accreted toward the end of the infall phase was isotopically distinct allows us to explain the observed dichotomy in nucleosynthetic isotopic anomalies of meteorites. It leads us toward intriguing predictions on the possible isotopic composition of refractory elements in comets. At a later time, when the infall of material waned, the disk started to evolve as an accretion disk. Initially, dust drifted inward, shrinking the radius of the dust component to ∼45 au, probably about to about half of the width of the gas component. Next, structures must have emerged, producing a series of pressure maxima in the disk, which trapped the dust on Myr timescales. This allowed planetesimals to form at radically distinct times without significantly changing any of the isotopic properties. We also conclude that there was no late accretion of material onto the disk via streamers. The disk disappeared at about 5 My, as indicated by paleomagnetic data in meteorites.
Conclusions. The evolution of the protosolar disk seems to have been quite typical in terms of size, lifetime, and dust behavior. This suggests that the peculiarities of the Solar System with respect to extrasolar planetary systems probably originate from the chaotic nature of planet formation and not from the properties of the parental disk itself.
A consensus prevails with regard to star-disk systems accreting most of their mass and angular momentum during the collapse of a prestellar core. However, recent results have indicated that stars experience post-collapse or late infall, during which the star and its disk are refreshed with material from the protostellar environment through accretion streamers. Apart from adding mass to the star-disk system, infall potentially supplies a substantial amount of angular momentum, as the infalling material is initially not bound to the collapsing prestellar core. We investigate the orientation of infall on star-disk systems by analyzing the properties of accreting tracer particles in three-dimensional magnetohydrodynamical (3D MHD) simulations of a molecular cloud that is in volume. In contrast to the traditional picture, where the rotational axis is inherited from the collapse of a coherent pre-stellar core, the orientation of star-disk systems changes substantially throughout the accretion process, thereby extending the possibility of primordial misalignment as the source of large obliquities. In agreement with previous results that show larger contributions of late infall for increasing stellar masses, a misaligned infall is more likely to lead to a prolonged change in orientation for stars of higher final mass. On average, brown dwarfs and very low mass stars are more likely to form and accrete all of their mass as part of a multiple system, while stars with final masses above a few 0.1 M are more likely to accrete part of their mass as single stars. Finally, we find an overall trend among our sample: the post-collapse accretion phase is more anisotropic than the early collapse phase. This result is consistent with a scenario of Bondi-Hoyle-Littletlon accretion during the post-collapse phase, while the initial collapse is less anisotropic -- despite the fact that material is funneled through accretion channels.
We used the Five-hundred-meter Aperture Spherical radio Telescope (FAST) to search for the molecular emissions in the L-band between 1.0 and 1.5 GHz toward four comets, C/2020 F3 (NEOWISE), C/2020 R4 (ATLAS), C/2021 A1 (Leonard), and 67P/Churyumov-Gerasimenko during or after their perihelion passages. Thousands of molecular transition lines fall in this low-frequency range, many attributed to complex organic or prebiotic molecules. We conducted a blind search for the possible molecular lines in this frequency range in those comets and could not identify clear signals of molecular emissions in the data. Although several molecules have been detected at high frequencies of great than 100 GHz in comets, our results confirm that it is challenging to detect molecular transitions in the L-band frequency ranges. The non-detection of L-band molecular lines in the cometary environment could rule out the possibility of unusually strong lines, which could be caused by the masers or non-LTE effects. Although the line strengths are predicted to be weak, for FAST, using the ultra-wide bandwidth receiver and improving the radio frequency interference environments would enhance the detectability of those molecular transitions at low frequencies in the future.
The formation of protostars and their disks has been understood as the result of the gravitational collapse phase of an accumulation of dense gas that determines the mass reservoir of the star-disk system. Against this background, the broadly applied scenario of considering the formation of disks has been to model the collapse of a dense core assuming spherical symmetry. Our understanding of the formation of star-disk systems is currently undergoing a reformation though. The picture evolves from interpreting disks as the sole outcome of the collapse of an isolated prestellar core to a more dynamic picture where disks are affected by the molecular cloud environment in which they form. In this review, we provide a status report of the state-of-the-art of spherical collapse models that are highly advanced in terms of the incorporated physics together with constraints from models that account for the possibility of infall onto star-disk systems in simplified test setups, as well as in multi-scale simulations that cover a dynamical range from the Giant Molecular Cloud environment down to the disk. Considering the observational constraints that favor a more dynamical picture of star formation, we finally discuss the challenges and prospects in linking the efforts of tackle the problem of star-disk formation in combined multi-scale, multi-physics simulations.
Context . The outcome of the formation of massive stars is an important anchor point in the formation and evolution process of these stars. It provides insight into the physics of the assembly process, and sets the conditions for stellar evolution. For massive stars, the outcome of formation is rarely observed because the processes involved unfold deep down in highly extincted molecular clouds.
Aims . We characterize a population of highly reddened stars in the very young massive star-forming region M17. The group of 18 O4.5 to B9 stars constitutes one of the best samples of almost zero-age main-sequence (ZAMS) high- and intermediate-mass stars. Their properties allow us to identify the empirical location of the ZAMS of massive stars, and the rotation and mass-loss rate of stars close to or at the onset of core-hydrogen burning.
Methods . We performed quantitative spectroscopic modeling of a uniform set of over 100 spectral features in optical VLT/X-shooter spectra using the nonlocal thermal equilibrium stellar atmosphere code F ASTWIND and a fitting approach based on a genetic algorithm, K IWI -GA. The spectral energy distributions of photometric observations were used to determine the line-of-sight extinction. From a comparison of their positions in the Hertzsprung-Russell diagram with MIST evolutionary tracks, we inferred the stellar masses and ages.
Results . We find an age of 0.4 −0.2 +0.6 Myr for our sample, however we also identify a strong relation between the age and the mass of the stars. All sources are highly reddened, with A V ranging from 3.6 to 10.6 mag. The sample can be subdivided into two groups. Stars more massive than 10 M ⊙ have reached the ZAMS. Their projected ZAMS spin rate distribution extends to 0.3 of the critical velocity; their mass-loss rates agree with those of other main-sequence O and early-B stars. Stars with a mass in the range 3 < M /M ⊙ < 7 are still on the pre-main sequence (PMS), and some of them have circumstellar disks. Evolving their υ sin i to the ZAMS assuming angular momentum conservation yields values up to ~0.6 υ crit . For PMS stars without disks, we find tentative mass-loss rates up to 10 −8.5 M ⊙ yr ⁻¹ . The total-to-selective extinction R V is higher for PMS stars with disks than for the remainder of the sample.
Conclusions . We constrain the empirical location of the ZAMS for massive (10 < M /M ⊙ < 50) stars and find it to agree with its location in MIST evolutionary tracks. The ZAMS rotation rates for intermediate-mass stars are twice as high as for massive stars, suggesting that the angular momentum gain processes differ between the two groups. The relation between the age and mass of the stars suggests a lag in the formation of more massive stars relative to lower mass stars. Taking the derived mass-loss rates at face value, stellar winds are already initiated in the PMS phase. The PMS-star winds are found to be substantially more powerful than indicated by predictions for line-driven outflows.
Context . Molecular clouds are the most important incubators of young stars clustered in various stellar structures whose spatial extension can vary from a few AU to several thousand AU. Although the reality of these stellar systems has been established, the physical origin of their multiplicity remains an open question.
Aims . Our aim was to characterise these stellar groups at the onset of their formation by quantifying both the number of stars they contain and their mass using a hierarchical fragmentation model of the natal molecular cloud.
Methods . We developed a stochastic and predictive model that reconciles the continuous multi-scale structure of a fragmenting molecular cloud with the discrete nature of the stars that are the products of this fragmentation. In this model a gas structure is defined as a multi-scale object associated with a subregion of a cloud. Such a structure undergoes quasi-static subfragmentation until star formation. This model was implemented within a gravo-turbulent fragmentation framework to analytically follow the fragmentation properties along spatial scales using an isothermal and adiabatic equations of state (EOSs).
Results . We highlighted three fragmentation modes depending on the amount of fragments produced by a collapsing gas structure, namely a hierarchical mode, a monolithic mode, and a mass dispersal mode. Using an adiabatic EOS we determined a characteristic spatial scale where further fragmentation is prevented, around a few tens of AU. We show that fragmentation is a self-regulated process as fragments tend to become marginally unstable following a M ∝ R Bonnor–Ebert-like mass-size profile. Supersonic turbulent fragmentation structures the cloud down to R ≈ 0.1 pc, and gradually turns into a less productive Jeans-type fragmentation under subsonic conditions so hierarchical fragmentation is a scale dependant process.
Conclusions . Our work suggests that pre-stellar objects resulting from gas fragmentation, have to progressively increase their accretion rate in order to form stars. A hierarchical fragmentation scenario is compatible with both the multiplicity of stellar systems identified in Taurus and the multi-scale structure extracted within NGC 2264 molecular cloud. This work suggests that hierarchical fragmentation is one of the main mechanisms explaining the presence of primordial structures of stellar clusters in molecular clouds.
Context . The star formation rate (SFR), the number of stars formed per unit of time, is a fundamental quantity in the evolution of the Universe.
Aims . While turbulence is believed to play a crucial role in setting the SFR, the exact mechanism remains unclear. Turbulence promotes star formation by compressing the gas, but also slows it down by stabilizing the gas against gravity. Most widely used analytical models rely on questionable assumptions, including: i ) integrating over the density PDF, a one-point statistical description that ignores spatial correlation, ii ) selecting self-gravitating gas based on a density threshold that often ignores turbulent dispersion, iii ) assuming the freefall time as the timescale for estimating SFR without considering the need to rejuvenate the density PDF, iv ) assuming the density probability distribution function (PDF) to be log-normal. This leads to the reliance on fudge factors for rough agreement with simulations. Even more seriously, when a more accurate density PDF is being used, the classical theory predicts a SFR that is essentially 0.
Methods . Improving upon the only existing model that incorporates the spatial correlation of the density field, we present a new analytical model that, in a companion paper, is rigorously compared against a large series of numerical simulations. We calculate the time needed to rejuvenate density fluctuations of a given density and spatial scale, revealing that it is generally much longer than the freefall time, rendering the latter inappropriate for use.
Results . We make specific predictions regarding the role of the Mach number, ℳ, and the driving scale of turbulence divided by the mean Jeans length. At low to moderate Mach numbers, turbulence does not reduce and may even slightly promote star formation by broadening the PDF. However, at higher Mach numbers, most density fluctuations are stabilized by turbulent dispersion, leading to a steep drop in the SFR as the Mach number increases. A fundamental parameter is the exponent of the power spectrum of the natural logarithm of the density, ln ρ , characterizing the spatial distribution of the density field. In the high Mach regime, the SFR strongly depends on it, as lower values imply a paucity of massive, gravitationally unstable clumps.
Conclusions . We provide a revised analytical model to calculate the SFR of a system, considering not only the mean density and Mach number but also the spatial distribution of the gas through the power spectrum of ln ρ , as well as the injection scale of turbulence. At low Mach numbers, the model predicts a relatively high SFR nearly independent of ℳ, whereas for high Mach, the SFR is a steeply decreasing function of ℳ.
First stars play crucial roles in the development of the Universe, influencing events like cosmic reionization and the chemcal enrichment of the intergalactic medium. While first stars are conventionally thought to form at around –30 in the standard cold dark matter (CDM) cosmology, observational constraints on small-scale (Mpc) density fluctuations remain limited, possibly differing significantly from the scale-invariant fluctuations assumed in the CDM model. Should this be the case, the formation of first stars could occur much earlier than typically predicted. In this study, we investigate the formation process of first stars in the extremely early epochs of in the post-recombination Universe. At such early times, the effects of the warm cosmic microwave background (CMB) become significant. We calculate the collapse of primordial star-forming clouds using a one-zone thermo-chemical model that accounts for CMB influences on radiative heating, Compton cooling, and photodissociation reactions. We found that the impact of the CMB on the evolution is limited at , with the temperature evolution closely resembling the conventional model. However, within the range , the formation of H via the H channel is impeded by H photo-detachment induced by the CMB, leading to higher temperatures compared to standard thermal evolution. Consequently, first stars with masses exceeding can emerge at . Furthermore, at , the temperature evolution becomes nearly isothermal at several thousand Kelvin solely due to atomic cooling, as H formation is entirely suppressed, including the less-efficient H channel, which is blocked by H photodissociation. In such cases, supermassive stars with masses around are expected to form solely via atomic cooling. These findings emphasize the significant variation in the typical mass of the first stars depending on the epoch of formation.
In order to develop a complete theory of star formation, one essentially needs to know two things: what collapses and how long it takes. This is the second paper in a series, where we query how long a parcel of gas takes to collapse and the process it undergoes. We embed pseudo-Lagrangian tracer particles in simulations of collapsing molecular clouds, identify the particles that end in dense knots, and then examine the collapse history of the gas. We find a nearly universal behaviour of cruise-then-collapse, wherein a core stays at intermediate densities for a significant fraction of its life before finally collapsing. We identify time immediately before each core collapses, , and examine how it transitions to high density. We find that the time to collapse is uniformly distributed between and the end of the simulation at , and that the duration of collapse is universally short, , where is the free-fall time at the mean density. We describe the collapse in three stages: collection, hardening, and singularity. Collection sweeps low-density gas into moderate density. Hardening brings kinetic and gravitational energies into quasi-equipartition. Singularity is the free-fall collapse, forming an envelope in rough energy balance and central overdensity in .
The formation of protostars and their disks has been understood as the result of the gravitational collapse phase of an accumulation of dense gas that determines the mass reservoir of the star-disk system. Against this background, the broadly applied scenario of considering the formation of disks has been to model the collapse of a dense core assuming spherical spherical symmetry. Our understanding of the formation of star-disk systems is currently undergoing a reformation though. The picture evolves from interpreting disks as the sole outcome of the collapse of an isolated prestellar core to a more dynamic picture where disks are affected by the molecular cloud environment in which they form. In this review, we provide a status report of the state-of-the-art of spherical collapse models that are highly advanced in terms of the incorporated physics together with constraints from models that account for the possibility of infall onto star-disk systems in simplified test setups, as well as in multi-scale simulations that cover a dynamical range from the Giant Molecular Cloud environment down to the disk. Considering the observational constraints that favor a more dynamical picture of star formation, we finally discuss the challenges and prospects in linking the efforts of tackle the problem of star-disk formation in combined multi-scale, multi-physics simulations.
Context. The extent of the coupling between the magnetic field and the gas during the collapsing phase of star-forming cores is strongly affected by the dust size distribution, which is expected to evolve by means of coagulation, fragmentation, and other collision outcomes.
Aims. We aim to investigate the influence of key parameters on the evolution of the dust distribution, as well as on the magnetic resistivities during protostellar collapse.
Methods. We performed a set of collapsing single-zone simulations with shark . The code computes the evolution of the dust distribution, accounting for different grain growth and destruction processes, with the grain collisions being driven by brownian motion, turbulence, and ambipolar drift. It also computes the charges carried by each grain species and the ion and electron densities, as well as the magnetic resistivities.
Results. We find that the dust distribution significantly evolves during the protostellar collapse, shaping the magnetic resistivities. The peak size of the distribution, population of small grains, and, consequently, the magnetic resistivities are controlled by both coagulation and fragmentation rates. Under standard assumptions, the small grains coagulate very early as they collide by ambipolar drift, yielding magnetic resistivities that are many orders of magnitude apart from the non-evolving dust case. In particular, the ambipolar resistivity, η AD , is very high prior to n H = 10 ¹⁰ cm ⁻³ . As a consequence, magnetic braking is expected to be ineffective. In this case, large size protoplanetary discs should result, which is inconsistent with recent observations. To alleviate this tension, we identified mechanisms that are capable of reducing the ambipolar resistivity during the ensuing protostellar collapse. Among them, electrostatic repulsion and grain-grain erosion feature as the most promising approaches.
Conclusions. The evolution of the magnetic resistivities during the protostellar collapse and consequently the shape of the magnetic field in the early life of the protoplanetary disc strongly depends on the possibility to repopulate the small grains or to prevent their early coagulation. Therefore, it is crucial to better constrain the collision outcomes and the dust grain’s elastic properties, especially the grain’s surface energy based on both theoretical and experimental approaches.
The envelopes and disks that surround protostars reflect the initial conditions of star and planet formation and govern the assembly of stellar masses. Characterizing these structures requires observations that span the near-IR to centimeter wavelengths. Consequently, the past two decades have seen progress driven by numerous advances in observational facilities across this spectrum, including the Spitzer Space Telescope , Herschel Space Observatory , the Atacama Large Millimeter/submillimeter Array, and a host of other ground-based interferometers and single-dish radio telescopes. ▪ Nearly all protostars have well-formed circumstellar disks that are likely to be rotationally supported; the ability to detect a disk around a protostar is more a question of spatial resolution rather than whether or not a disk is present.
▪ The disks around protostars have inherently higher millimeter/submillimeter luminosities as compared to disks around more-evolved pre-main-sequence stars, though there may be systematic variations between star-forming regions.
▪ The envelopes around protostars are inherently asymmetric, and streamers emphasize that mass flow through the envelopes to the disks may not be homogeneous.
▪ The current mass distribution of protostars may be impacted by selection bias given that it is skewed toward solar-mass protostars, which is inconsistent with the stellar initial mass function.
The formation mechanism of massive stars remains one of the main open problems in astrophysics, in particular the relationship between the mass of the most massive stars and that of the cores in which they form. Numerical simulations of the formation and evolution of molecular clouds, within which dense cores and stars form self-consistently, show that the core mass increases in time, and also that the most massive stars tend to appear later than lower mass stars. We present an idealized model that incorporates accretion onto the cores as well as onto the stars, in which the core mass growth is regulated by a ‘gravitational choking’ mechanism that does not involve any form of support. This process is of purely gravitational origin, and causes some of the mass accreted onto cores to stagnate there, rather than being transferred to the stars. In addition, we estimate the mass of the most massive allowed star before its photoionizing radiation is capable of overcoming the accretion flow. This model constitutes a proof of concept for the simultaneous growth of the gas reservoir and the stellar mass, the delay in the formation of massive stars observed in numerical simulations, the need for massive, dense cores in order to form massive stars, and the observed correlation between the mass of the most massive star and the mass of the cluster it resides in. Also, our model implies that by the time massive stars begin to form in a core, a number of low-mass stars are expected to have already formed.
Stars are among the most fundamental structures of our Universe. They comprise most of the baryonic and luminous mass of galaxies; synthesize heavy elements; and inject mass, momentum, and energy into the interstellar medium. They are also home to the planets. Because stellar properties are primarily decided by their mass, the so-called stellar initial mass function (IMF) is critical to the structuring of our Universe. We review the various physical processes and theories that have been put forward as well as the numerical simulations that have been carried out to explain the origin of the stellar IMF. Key messages from this review include the following: ▪ Gravity and turbulence most likely determine the power-law, high-mass part of the IMF.
▪ Depending of the Mach number and the density distribution, several regimes are possible, including Γ IMF ≃ 0, −0.8, −1, or −1.3, where d N /d log M ∝ M Γ IMF . These regimes are likely universal; however, the transition between these regimes is not.
▪ Protostellar jets can play a regulating influence on the IMF by injecting momentum into collapsing clumps and unbinding gas.
▪ The peak of the IMF may be a consequence of dust opacity and molecular hydrogen physics at the origin of the first hydrostatic core. This depends weakly on large-scale environmental conditions such as radiation, magnetic field, turbulence, or metallicity. This likely constitutes one reason for the relative universality of the IMF.
Context . Recent observations of protostellar cores suggest that most of the material in the protostellar phase is accreted along streamers. Streamers in this context are defined as velocity coherent funnels of denser material potentially connecting the large-scale environment to the small scales of the forming accretion disk.
Aims . Using simulations that simultaneously resolve the driving of turbulence on the filament scale as well as the collapse of the core down to protostellar disk scales, we aim to understand the effect of the turbulent velocity field on the formation of overdensities in the accretion flow.
Methods . We performed a three-dimensional numerical study on a core collapse within a turbulent filament using the RAMSES code and analysed the properties of overdensities in the accretion flow.
Results . We find that overdensities are formed naturally by the initial turbulent velocity field inherited from the filament and subsequent gravitational collimation. This leads to streams that are not really filamentary but show a sheet-like morphology. Moreover, they have the same radial infall velocities as the low density material. As a main consequence of the turbulent initial condition, the mass accretion onto the disk does not follow the predictions for solid body rotation. Instead, most of the mass is funneled by the overdensities to intermediate disk radii.
Over the past decade, advancement of observational capabilities, specifically the Atacama Large Millimeter/submillimeter Array (ALMA) and Spectro-Polarimetric High-contrast Exoplanet REsearch (SPHERE) instruments, alongside theoretical innovations like pebble accretion, have reshaped our understanding of planet formation and the physics of protoplanetary disks. Despite this progress, mysteries persist along the winded path of micrometer-sized dust, from the interstellar medium, through transport and growth in the protoplanetary disk, to becoming gravitationally bound bodies. This review outlines our current knowledge of dust evolution in circumstellar disks, yielding the following insights: ▪ Theoretical and laboratory studies have accurately predicted the growth of dust particles to sizes that are susceptible to accumulation through transport processes like radial drift and settling.
▪ Critical uncertainties in that process remain the level of turbulence, the threshold collision velocities at which dust growth stalls, and the evolution of dust porosity.
▪ Symmetric and asymmetric substructure are widespread. Dust traps appear to be solving several long-standing issues in planet formation models, and they are observationally consistent with being sites of active planetesimal formation.
▪ In some instances, planets have been identified as the causes behind substructures. This underlines the need to study earlier stages of disks to understand how planets can form so rapidly.
In the future, better probes of the physical conditions in optically thick regions, including densities, turbulence strength, kinematics, and particle properties will be essential for unraveling the physical processes at play.
The results of spectral observations in the GHz frequency range of six objects from the southern sky having dense cores and associated with massive star and star cluster forming regions are presented. The observations are carried out with the MOPRA-22m radio telescope. Within the framework of the local thermodynamic equilibrium (LTE) approximation, column densities and abundances of the H13CN, H13CO+, HN13C, HC3N, c-C3H2, SiO, CH3C2H and CH3CN molecules are calculated. Kinetic temperatures ( K), sizes of emission regions ( pc) and virial mass esimates () are obtained. The linewidths in the three cores decrease with increasing distance from the center. Four cores exhibit asymmetry in the profiles of the optically thick HCO+(1–0) and HCN(1–0) lines, indicating the presence of systematic motions in the line of sight. In two cases, the asymmetry can be caused by contraction of gas. The model HCO+(1–0) and H13CO+(1–0) spectral maps obtained within the non-LTE spherically symmetric model are fitted into observed ones. Radial density (), turbulent velocity () and contraction velocity () profiles in the G268.42–0.85 core are obtained. The contraction velocity radial profile differs from expected both in the case of free fall of gas onto a protostar (), and in the case of global core collapse (contraction velocity does not depend on distance). A discussion of the results obtained is provided.
The outstanding features of the strongly magnetic stars are (e.g. Ledoux and Renson 1966):(1)
Their apparent confinement mainly to stars of type A and earlier.
(2)
The presence of spectral anomalies: the magnetic A stars seem to be almost co-extensive with the peculiar A stars, with their abnormally high surface abundances of the rare earths, silicon, chromium, manganese, strontium, yttrium and zirconium.
(3)
The high field-strengths, inferred from the Zeeman effect: typical polar fields are 103–104 gauss, with the strongest known being 35,000 gauss.
(4)
The variability of the fields, spectra and luminosities. The fields are often found to reverse in sign. Typical periods are 5–9 days, but periods both shorter and very much longer are found, a few stars having periods of several years.
(5)
The low rotations of the A stars as compared with normal A stars. This is inferred from statistical analysis of spectral line-widths.
The gross internal dynamics of interstellar clouds are studied by means of the tensor virial equations. To evaluate the virial integrals, clouds are approximated as compressible ellipsoids, uniform in density, bounded by external pressure, and with velocities linear in the coordinates. Rigidly rotating spheroidal equilibrium states exist for any external pressure, but those at high pressure are distortionally unstable. Elongated rigidly rotating equilibria also exist, but not if the external pressure is sufficiently high. Numerical integration of the dynamic equations demonstrates that clouds of low angular momentum can collapse by several orders of magnitude in density even while remaining axially symmetric. Collapse with the conservation of angular momentum is also possible for clouds of high angular momentum if they attain a specific elongated configuration. The transition between the behavior of clouds of low and high angular momentum is surprisingly abrupt.
The evolution of collapsing protostars of 0.05, 1 and 20M⊙ is studied with computations which include radiative as well as convective energy flow, which has been entirely neglected
in previous papers I and II. It is found that, when a shock wave which has been generated at the center reaches the outermost
layers, the protostars flare up suddenly.
The protostar of 1M⊙ increases its luminosity from 5 ×10-4 L⊙ to a peak value 6 ×103 L⊙ in a period of the order of 10 days. This peak value depends scarcely on the initial conditions. After the flare-up, a convective
region grows inwards from the surface and the luminosity is kept at 1 ×103 L⊙ by convection until the star finally reaches a stage of wholly gravitational equilibtium.
The luminosity at this stage is found to be very sensitive to the stellar mass, being 8L⊙ and 5 ×104 L⊙ for the protostars of 0.05 and 20M⊙. respectively. These computed values of the luminosity are high enough to cover the observations of infrared objects.
Some of the more important aspects of research on dark nebulae, globules, and protostars are reported. Included are the birth of a star in the galaxy, optical and radio evidence for large globules and their evolutionary status, and star formation in the star clouds of Magellan. 51 references. (JFP)
Two-dimensional hydrodynamical calculations are presented to demonstrate a mechanism of star formation which, within the context of the spiral density wave theory, can explain the narrowness of the spiral arms of galaxies delineated by the classic spiral tracers: the bright, young stars and their associated H II regions. The implosion of a standard interstellar cloud has been followed numerically after it encounters a shock in the intercloud medium. Parameters have been chosen to represent a cloud flowing into a spiral arm which is delineated by a shock in the interstellar gas. Although this work is motivated by spiral wave theory, the results should also be indicative of the evolution of a cloud struck, for example, by a supernova shock.
A numerical scheme is developed in which rapid dynamic motion in one
part of a protostar and quasi-static evolution in another part can be
calculated simultaneously. Based on this technique, the evolution of
spherically symmetric protostars with initial masses between 0.1 and 50
solar masses is investigated. The general evolutionary features are
found to be similar to those of previous models, but the final
hydrostatic-equilibrium configurations have large radii as compared to
Larson's (1973) protostar models. It is found for low-mass protostars
that the luminosity remains relatively low until late evolutionary
stages and that evolution is very sensitive to the treatment of
convective energy transport. For high-mass protostars, it is found that
a convective phase never exists and that a fraction of the initial mass
is ejected due to heating and radiation pressure in the envelope.
Detailed numerical results are given for a protostar with 1 solar mass,
and some observational implications of this work are discussed.
Hydrodynamic model computations have been carried out for a spherically
symmetric protostar of one solar mass. Compared to similar computations
by Larson (1969), different treatment of the accretion shock front is
used. The computations basically confirm Larson's results and show that
Larson's disputed shock jump conditions have little influence on the
protostellar models.
Numerical calculations of the dynamics of a spherically symmetric collapsing proto-star of one solar mass have been made for
various initial conditions. Calculations have also been made for masses of 2M⊙ and 5M⊙. In all cases the collapse is found to be extremely non-homologous and is such that a very small part of the cloud's mass
at the centre reaches stellar densities and stops collapsing before most of the cloud has had time to collapse very far. The
stellar core thus formed subsequently grows in mass as material falls into it, finally becoming an ordinary star when all
of the proto-stellar material has been accreted. During most of this time the stellar core is completely obscured by the dust
in the infalling cloud, the absorbed radiation reappearing in the infra-red as thermal emission from the dust grains. The
resulting star is almost a conventional Hayashi pre-main sequence model, but it appears rather low on the Hayashi track. For
masses much greater than about 2M⊙ the convective Hayashi phase does not exist at all. It appears that certain properties of T Tauri stars may find explanation
in the results of the present calculations.
In an appendix to the paper it is shown that limiting forms may be derived for the density and velocity distributions near
the centre of an isothermally collapsing sphere. This may be shown to be possible also for a sphere with a polytropic equation
of state. Numerical results are presented for the limiting solution in the isothermal case.
For a cold gas, the analytical solutions for collapse in various symmetries give density and velocity profiles at the instant
when a singularity develops in the initially densest part. These profiles follow generally from assuming that the density
variation is smooth initially. For spherical and planar symmetries we have extended these solutions to a short time before
this singularity occurs.
The spherical results are given in Sections 2–4 and imply a density law proportional to r–12/7. The planar results follow in Appendix I and the cylindrical ones in Appendix II. The solutions before the singularity arises
are similarity solutions with the density and velocity profiles retaining their shapes while altering only their scales with
time.
Applying these results we find a spherical collapse to form a galaxy is modified by the rise in central optical depth at a
density of ~ 10–20 g cm–3. Flattening instabilities are resisted but not overcome by the more rapid growth of the density gradient which occurs in
a planar collapse.
In Section 5, a similarity solution for the spherical collapse of an isothermal gas is presented. This has a critical point
similar to those found in solar wind flows. The density profile when the singularity arises is proportional to r–2. The collapse of a proto-star is halted by the rise in optical depth when the density reaches 10–18 g cm–3. The stability of this solution and the problem of whether all flows converge to it still remain to be settled.
The special accretion problem is investigated in which the motion is steady and spherically symmetrical, the gas being at
rest at infinity. The pressure is taken to be proportional to a power of the density. It is found that the accretion rate
is proportional to the square of the mass of the star and to the density of the gas at infinity, and varies inversely with
the cube of the velocity of sound in the gas at infinity. The factor of proportionality is not determined by the steady-state
equations, though it is confined within certain limits. Arguments are given suggesting that the case physically most likely
to occur is that with the maximum rate of accretion.
On spine: Early stages of star formation. Thesis--Princeton University. Includes bibliographical references (leaves [53]-[55]). Photocopy of typescript. Ann Arbor, Mich. : University Microfilms, 1976. 21 cm.
The paper studies the equilibrium of self-gravitating isothermal models of interstellar clouds with a frozen-in magnetic field linked smoothly to the field of a hot tenuous intercloud medium. Equilibrium states are determined which can be reached by clouds contracting nonhomologously from a spherical uniform initial state. Three free parameters characterize the problem: a dimensionless initial radius related to the Jeans length of the cloud, the initial ratio of the magnetic and gas pressures in the cloud, and the initial ratio of the intercloud and cloud pressures. The dependence of the solutions on each of these parameters is investigated. It is found that: (1) the frozen-in field causes the cloud to become oblate with its major axis normal to the field lines; (2) the flattening increases as the magnetic-field strength, gravitational forces, or intercloud pressure increases; (3) increasing intercloud pressure eventually leads to gravitational collapse; and (4) the cloud can reach equilibrium only if its radius does not exceed some critical value. The observed inefficiency of the star-formation process within massive clouds is examined and explained in terms of magnetic phenomena in a collapsing cloud.